weibull_family: Weibull Family for Survival Model Specification

In lgspline: Lagrangian Multiplier Smoothing Splines for Smooth Function Estimation

Weibull Family for Survival Model Specification

Description

Creates a family-like object for Weibull accelerated failure time (AFT) models, including custom log-likelihood, AIC, and deviance helpers.

This both provides a tool for actually fitting Weibull AFT Models, and boilerplate code for users who wish to incorporate Lagrangian multiplier smoothing splines into their own custom models.

Usage

weibull_family()

Details

Provides a comprehensive family specification for Weibull AFT models, including family name, link function, inverse link function, custom loss function for model tuning, and methods for AIC and log-likelihood computation compatible with logLik.lgspline.

Supports right-censored survival data with flexible parameter estimation.

Note on scale vs. dispersion: throughout this package, the lgspline object stores sigmasq_tilde which equals sigma^2 (dispersion), where sigma is the Weibull scale parameter matching survreg$scale. Functions that accept a dispersion argument receive sigma^2; functions that accept a scale argument receive sigma.

Value

A family-like list containing the link functions and Weibull-specific methods used by lgspline.

Examples

## Simulate survival data with covariates
set.seed(1234)
n <- 1000
t1 <- rnorm(n)
t2 <- rbinom(n, 1, 0.5)

## Generate survival times with Weibull-like structure
lambda <- exp(0.5 * t1 + 0.3 * t2)
yraw <- rexp(n, rate = 1/lambda)

## Introduce right-censoring
status <- rbinom(n, 1, 0.75)
y <- ifelse(status, yraw, runif(length(yraw), 0, yraw))

## Prepare data
df <- data.frame(y = y, t1 = t1, t2 = t2, status = status)

## Fit model using custom Weibull family
model_fit <- lgspline(y ~ spl(t1) + t2,
                      df,
                      unconstrained_fit_fxn = unconstrained_fit_weibull,
                      family = weibull_family(),
                      need_dispersion_for_estimation = TRUE,
                      dispersion_function = weibull_dispersion_function,
                      glm_weight_function = weibull_glm_weight_function,
                      schur_correction_function = weibull_schur_correction,
                      status = status,
                      opt = FALSE,
                      K = 1)

summary(model_fit)

## Log-likelihood now works via logLik.lgspline:
# logLik(model_fit)

lgspline documentation built on Aug. 5, 2026, 1:10 a.m.